If n(A ∩ Bᶜ) = 48, n(Aᶜ ∩ B) = 44, n(A ∩ B) = 28, and n(U) = 160, what is n(Aᶜ ∩ Bᶜ)?
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Answer and explanation
Correct answer: 40
The universal set is divided into four mutually exclusive Venn-diagram regions: A ∩ Bᶜ, Aᶜ ∩ B, A ∩ B, and Aᶜ ∩ Bᶜ. The first three regions contain 48 + 44 + 28 = 120 elements. Since the universal set contains 160 elements, the remaining region is n(Aᶜ ∩ Bᶜ) = 160 − 120 = 40. Thus, option B is correct.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The universal set is divided into four mutually exclusive Venn-diagram regions: A ∩ Bᶜ, Aᶜ ∩ B, A ∩ B, and Aᶜ ∩ Bᶜ. The first three regions contain 48 + 44 + 28 = 120 elements. Since the universal set contains 160 elements, the remaining region is n(Aᶜ ∩ Bᶜ) = 160 − 120 = 40. Thus, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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